JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (6): 103-107.doi: 10.6040/j.issn.1671-9352.0.2022.627

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Number of homomorphisms between finitely generated Abelian groups and finite groups

Yanxia LI(),Jinke HAI*()   

  1. College of Mathematics and Statistics, Qingdao University, Qingdao 266071, Shandong, China
  • Received:2022-11-18 Online:2024-06-20 Published:2024-06-17
  • Contact: Jinke HAI E-mail:yanxialiqdu@163.com;haijinke2002@aliyun.com

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Abstract:

Let $G$ be a finite group, and $F=F_{r} \times A$ be a finitely generated Abelian group, where $A$ is finite and $F_{r}$ is a free Abelian group of rank $r$. It is proved that the number of homomorphisms from $F$ to $G$ is a multiple of $|A|$ and $|G|$ greatest common divisor. The results generalize the famous T.Yoshdia theorem.

Key words: group homomorphism, group action, free Abelian group

CLC Number: 

  • O152.1
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